Proceedings of the IASTED International Conference Artificial Intelligence and Applications (AIA 2014) February 17 - 19, 2014 Innsbruck, Austria TOWARDS THE SELF-ADAPTATION OF THE BAT ALGORITHM Iztok Fister Jr.a, Simon Fongb, Janez Bresta, Iztok Fistera a University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova 17, 2000 Maribor, Slovenia Email: iztok.fi[email protected], [email protected], iztok.fi[email protected] b University of Macau, Faculty of Science and Technology, Av. Padre Tomas Pereira, Taipa, Macau SAR Email: [email protected] ABSTRACT the natural behavior of different biological systems in or- Bat algorithm is one of the younger members of swarm in- der to solve particular problems using the digital comput- telligence algorithms that was introduced by Yang in 2010. ers. Adaptation is one of the more important characteristic So far, several variants based on this algorithm have been for surviving the individuals in biological systems that are proposed for coping with the continuous and discrete prob- subject to ruthless changing environment [8]. This mecha- lems. This paper introduces a novel self-adaptive bat algo- nism enables the individuals in biological systems to adapt rithm (SABA) that borrows the self-adapting mechanism themselves to the changing conditions within their environ- from self-adapted differential evolution known under the ments. The adaptation is not just a unique characteristic of name jDE. This algorithm was tested on ten benchmark the biological systems, because this mechanism has also functions taken from publications. The obtained results been incorporated into artificial systems and optimization were very promising and showed that this algorithm might algorithms. be very suitable for use, especially, in the continuous opti- The optimization algorithms are controlled by algo- mization. rithm parameters that can be changed deterministically, adaptively, and self-adaptively [9]. Deterministic param- KEY WORDS eters are altered by using some deterministic rule (e.g., bat algorithm, swarm intelligence, optimization, self- Rechenberg’s 1/5 success rule [10]). In contrast, adap- adaptation tive controlled parameters are subject to feedback from the search process that serves as an input to a mechanism 1 Introduction used that determines the direction and magnitude of the change [9]. Finally, the self-adaptive controlled parameters Nowadays, optimization has become more and more im- are encoded into representation of solution and undergo portant in domains, like finances, industries, sport, phar- acting the variation operators, like crossover and mutation macy, etc. The task of the optimization is to find the mini- in evolutionary algorithms [11]. mum or maximum of objective function relating to a prob- This paper proposes a self-adaptive bat algorithm lem that needs to be solved. Typically, the minimal costs (SABA) for continuous optimization. However, this self- of production are searched for in many industries. For ex- adaptive variant of a bat algorithm (BA) can also be later ample, the problem of how to finish a specific work order applied to real-world problems. An origin of the BA algo- with minimal material usage has arisen in the clothing in- rithm goes to the year 2010, when Xin-She Yang [12, 13, dustry [1]. However, the clothing industry is not alone ex- 14] created a new optimization algorithm inspired by the ample. behavior of micro-bats that use a special mechanism called The similar optimization problems have been arisen echolocation. Echolocation is used by bats for orientation in many industries that are efficiently solved using the well- and prey seeking. The original BA was applied to vari- known algorithms, like: ous benchmark functions, in which it achieved the good • artificial bee colony [2], results. The convergence rate was improved in study [3], where the authors hybridized the original BA with differ- • bat algorithm [3], ential evolution strategies (HBA). On the other hand, Wang and Guo [15] successfully hybridized the BA with a har- • differential algorithm [4], mony search (HS/BA) [16]. • firefly algorithm [5], The original bat algorithm employs two strategy pa- rameters: the pulse rate and the loudness. The former reg- • particle swarm optimization [6], and ulates an improving of the best solution, while the later • many more [7]. influences an acceptance of the best solution. Both the mentioned parameters are fixed during the execution of the The mentioned algorithms are generally inspired by original bat algorithm. In SABA, these parameters are self- nature. In these algorithms, developers wish to mimics adapted. The aim of this self-adaptation is twofold. On the DOI: 10.2316/P.2014.816-011 400 one hand, it is very difficult to guess the valid value of the Algorithm 1 Pseudo-code of the original bat algorithm T parameter. On the other hand, this value depends on the Input: Bat population xi = (xi1; : : : ; xiD) for i = phase in which the search process is. This means, the pa- 1 ::: Np; MAX FE. rameter setting at the beginning of the search process can Output: The best solution xbest and its corresponding be changed, when this process becomes matured. There- value fmin = min(f(x)). fore, the self-adaptation of these parameters is applied in 1: init bat(); SABA. 2: eval = evaluate the new population; The proposed SABA algorithm were applied to an 3: fmin = find best solution(xbest ); finitializationg optimization of a benchmark function suite consisting of 4: while termination condition not meet do 10 well-known functions from the publications. The ob- 5: for i = 1 to Np do tained results using SABA improved the results achieved 6: y = generate new solution(xi); by the original BA. Additionally, the proposed algorithm 7: if rand(0; 1) > ri then was compared also with the other well-known algorithms, 8: y = improve the best solution(xbest ) like firefly (FA) [5], differential evolution (DE) [17], and 9: end iff local search step g artificial bee colony (ABC) [18]. The results from this com- 10: fnew = evaluate new solution(y); parison showed that the results of the SABA are compara- 11: eval = eval + 1; ble with the results of the other up-to-date algorithms. 12: if fnew ≤ fi and N(0; 1) < Ai then The structure of this paper is as follows. Section 2 13: xi = y; fi = fnew; presents the original bat algorithms. The self-adaptive bat 14: end iff save best solution conditionaly g algorithm is described in Section 3. Section 4 illustrates 15: fmin =find best solution(xbest ); the experiments and results detailed. The paper concludes 16: end for by summarizing the performed work and outlines further 17: end while directions for development. 2 The original bat algorithm operation of the original BA algorithm presented in Algo- rithm 1 can be described as follows. In general, the algo- The original bat algorithm was developed in 2010 by Xin- rithm consists of the following components [19]: She Yang [12, 13, 14]. The inspiration for his work came from behavior of micro-bats and especially, their special • initialization (lines 1-3): initializing the algorithm pa- mechanism named echolocation. Echolocation is a mech- rameters, generating the initial population, evaluating anism that bats use for orientation and finding the preys. it, and searching for the best solution xbest in the ini- Bats are not the only creatures using such a mechanism. tial population, For instance, dolphins use this mechanism for finding prey • generate new solution (line 6): moving the virtual in the seas [19]. bats in the search space according to physical rules Nowadays, BA and its variants are applied for solv- of bat echolocation, ing many optimization and classification problems, as well as several engineering problems in practice. In detail, the • local search step (lines 7-9): improving the best so- taxonomy of the developed BA applications is represented lution using random walk direct exploitation (RWDE) in [19], where the applications of BA algorithms have been heuristic [20], divided into the following classes of optimization prob- lems: continuous, constrained, and multi-objective. In ad- • evaluate new solution (line 10): evaluating the new dition, they were also used for classification problems, like solution, clustering, neural networks, and feature selection. Finally, • save best solution conditionaly (lines 12-14): saving BAs were used in many branches of engineering, e.g., im- the new best solution under some probability A sim- age processing, industrial design, scheduling, electronics, i ilar to simulated annealing [21], spam filtering, and even in sport. The original bat algorithm is population based, where • find best solution (line 15): searching for the current each individual represents the candidate solution. The best solution. candidate solutions are represented as vectors xi = T (xi1; : : : ; xiD) for i = 1 ::: Np with real-valued elements Note that these components are denoted in the al- xij, where each elements can capture values from interval gorithm either as function names, when the function call xij 2 [xlb; xub]. Thus, xlb and xub denote the correspond- is performed in one line or as a component name desig- ing lower and upper bound, while the population size is nated by a comment between two curly brackets, when determined by Np parameter. it comprises more lines. Initialization of the bat popula- The pseudo-code of the original BA algorithm is il- tion consist of tree steps. At first, the population is ini- lustrated in Algorithm 1, where bats’ behavior is captured tialized randomly (in function init bat). Then, solutions within the fitness function of the problem to be solved. The are evaluated (in function evaluate the new population) 401 and finally, the current best solution is found (in function 3 The self-adaptive bat algorithm find best solution). Generating the new solutions is per- formed according to the following equations: Self-adaptation of control parameters means that the algo- rithms control parameters (also strategy parameters) are en- coded into representation of a candidate solution and un- dergo acting the variation operators.